We carry out density-matrix-renormalization group (DMRG) calculations for the problem of one doped hole in a two-leg t-J ladder. Recent studies have concluded that exotic "Mott" physics-arising from the projection onto the space of no double-occupied sites-is manifest in this model system, leading to charge localization and a new mechanism for charge modulation. In contrast, we show that there is no localization and that the charge-density modulation arises when the minimum in the quasiparticle dispersion moves away from π. Although singular changes in the quasiparticle dispersion do occur as a function of model parameters, all of the DMRG results can be qualitatively understood from a noninteracting "band-structure" perspective.
We carry out density-matrix-renormalization group (DMRG) calculations for the problem of one doped hole in a two-leg t-J ladder. Recent studies have concluded that exotic "Mott" physics-arising from the projection onto the space of no double-occupied sites-is manifest in this model system, leading to charge localization and a new mechanism for charge modulation. In contrast, we show that there is no localization and that the charge-density modulation arises when the minimum in the quasiparticle dispersion moves away from π. Although singular changes in the quasiparticle dispersion do occur as a function of model parameters, all of the DMRG results can be qualitatively understood from a noninteracting "band-structure" perspective.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
Variational wave function for an anisotropic single-hole-doped t-J ladder
Based on three general guiding principles, i.e., no double occupancy constraint, accurate description of antiferromagnetism at half-filling, and the precise sign structure of the t-J model, a new ground state wave function has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this paper, we specifically study such kind of variational ground state for the one-hole-doped anisotropic two-leg t-J ladder using variational Monte Carlo (VMC) method. The results are then systematically compared with those recently obtained by density matrix renormalization group (DMRG) simulation. An excellent agreement is found between the VMC and DMRG results, including a "quantum critical point" at the anisotropy parameter α=αc≈0.7 (with the parameters t/J=3), and the emergence of charge modulation and momentum (Fermi point) reconstruction at α>αc due to the quantum interference of the sign structure. In particular, the wave function indicates that a Landau's quasiparticle description remains valid at ααc due to the breakdown of the one-to-one correspondence of momentum and translational symmetry of the hole. The explicit form of the wave function provides a direct understanding on how the many-body strong correlation effect takes place non-perturbatively in a doped Mott insulator, which sheds interesting light on the two-dimensional case where the same type of wave function was proposed to describe the cuprate superconductor.
The ground state of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ ladder with four legs favors a striped charge distribution for the parameters corresponding to hole-doped cuprate superconductors. We investigate the dynamical spin and charge structure factors of the model by using the dynamical density matrix renormalization group (DMRG) and clarify the influence of the stripe on the structure factors. The dynamical charge structure factor along the momentum direction from q=(0,0) to $(\ensuremath{\pi},0)$ clearly shows low-energy excitations corresponding to the stripe order in hole doping. On the other hand, the stripe order weakens in electron doping, resulting in fewer low-energy excitations in the charge channel. In the spin channel, we find incommensurate spin excitations near $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ forming an hourglass behavior in hole doping, while in electron doping we find clearly spin-wave-like dispersions starting from $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Along the $(0,0)\text{\ensuremath{-}}(\ensuremath{\pi},0)$ direction, the spin excitations are strongly influenced by the stripes in hole doping, resulting in two branches that form a discontinuous behavior in the dispersion. In contrast, the electron-doped systems show a downward shift in energy toward $(\ensuremath{\pi},0)$. These behaviors along the $(0,0)\text{\ensuremath{-}}(\ensuremath{\pi},0)$ direction are qualitatively similar to momentum-dependent spin excitations recently observed by resonant inelastic x-ray scattering experiments in hole- and electron-doped cuprate superconductors.
Quasiparticle collapsing is a central issue in the study of strongly correlated electron systems. In the one-dimensional case, the quasiparticle collapsing in a form of spin-charge separation has been well established, but the problem remains elusive in dimensions higher than one. By using the density matrix renormalization group (DMRG) algorithm, we show that in an anisotropic two-leg $t\ensuremath{-}J$ ladder, an injected single hole behaves like a well-defined quasiparticle in the strong rung limit but undergoes a ``phase transition'' with the effective mass diverging at a quantum critical point (QCP) towards the isotropic limit. After the transition, the quasiparticle collapses into a loosely bound object of a charge (holon) and a spin-1/2 (spinon) accompanied by an unscreened phase string as well as a substantially enhanced binding energy between two doped holes. A phase diagram of multileg ladders is further obtained, which extrapolates the QCP towards the two-dimensional limit. The underlying mechanism generic for any dimensions is also discussed.
The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole's motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system.
A long-standing issue in the physics of strongly correlated electronic systems is whether the motion of a single hole in quantum antiferromagnets can be understood in terms of the quasiparticle picture. Very recently, investigations of this issue have been within the experimental reach. Here we perform a large-scale density matrix renormalization group study, and provide the first unambiguous numerical evidence showing that in ladder systems, a single hole doped in the Mott antiferromagnet does not behave as a quasiparticle. Specifically, the injected hole is found to be always localized as long as the leg number is larger than one, with a vanishing quasiparticle weight and a localization length monotonically decreasing with the leg number. In addition, the single hole self-localization is insensitive to the parity (even-odd) of the leg number. Our findings may advance conceptual developments in different fields of condensed matter physics. First of all, the intriguing self-localization phenomenon is of pure strong correlation origin free of extrinsic disorders. Therefore, it is in sharp contrast to the well-known Anderson localization and recently found many-body localization, where extrinsic disordered potentials play crucial roles. Second, they confirm the analytical predictions of the so-called phase string theory, suggesting that the phase string effect lies in the core of the physics of doped Mott antiferromagnets.